TLDR: FLDmamba is a novel time series prediction framework that integrates Fourier and Laplace transforms with the Mamba architecture. It addresses key challenges in time series data, such as multi-scale periodicity, transient dynamics, and noise, which existing models struggle with. Through its unique design, FLDmamba achieves superior performance, enhanced robustness, and maintains computational efficiency, outperforming state-of-the-art Transformer and Mamba-based models in long-term forecasting across various real-world datasets.
Time series prediction, which involves forecasting future values based on historical data, is a critical task across many fields, from weather and traffic prediction to power grid management and stock markets. However, this domain faces significant challenges due to the inherent complexities of time series data, such as non-stationarity, patterns that repeat at different scales (multi-scale periodicity), sudden short-term changes (transient dynamics), and the presence of noise.
Existing predictive models, while advanced, struggle with these complexities, especially when making long-term predictions. Transformer-based architectures, popular in other AI fields, have been applied to time series but suffer from high computational costs, particularly with longer data sequences. More recently, State-Space Models like Mamba offer a more efficient alternative for long-term modeling. However, Mamba-based methods on their own have limitations: they don’t effectively capture multi-scale periodicity or transient dynamics, and they can be susceptible to data noise.
Introducing FLDmamba: A Novel Solution
To address these limitations, a new framework called FLDmamba (Fourier and Laplace Transform Decomposition Mamba) has been proposed. This innovative model integrates the strengths of both Fourier and Laplace transforms with the Mamba architecture to enhance time series prediction. The core idea is to leverage these mathematical transforms to better understand and model the complex characteristics of time series data.
How FLDmamba Works
FLDmamba incorporates several key technical advancements:
- Data Smoothing with Radial Basis Function (RBF) Kernel: Before processing, the input data is smoothed using an RBF kernel. This step helps reduce noise and allows the model to more accurately capture the underlying temporal patterns.
- Capturing Multi-Scale Periodicity with Fourier Analysis: Mamba primarily focuses on temporal dynamics. FLDmamba enhances this by integrating Fourier analysis, which operates in the frequency domain. This allows the model to identify and capture long-term properties like multi-scale periodic patterns that might be overlooked in the temporal domain. Fourier Transform also helps in separating underlying patterns from noise, making the model more robust.
- Modeling Transient Dynamics with Laplace Analysis: To better capture short-term fluctuations and time-varying patterns, FLDmamba introduces Laplace analysis. This integration helps the model understand relationships between neighboring data points and effectively model transient changes.
- The FMamba-Mamba (FMM) Block: FLDmamba combines its Fourier-enhanced Mamba (FMamba) and a standard Mamba encoder into a parallel FMM block. This integration allows the model to capture both periodic and transient dynamics simultaneously, while also helping to separate data noise.
- Inverse Laplace Transform for Prediction: The final predictions are generated using an inverse Laplace transform. This step is crucial for reconstructing the time-domain data, ensuring that both transient dynamics and long-term periodic trends are accurately reflected in the forecasts.
A significant advantage of FLDmamba is its computational efficiency. Despite its sophisticated architecture, FLDmamba maintains a computational complexity comparable to the base Mamba model, making it suitable for large-scale real-world applications.
Also Read:
- Enhancing Electricity Load Forecasting with Global Models and Smart Data Grouping
- Forecasting Future Dynamics with Vision Models
Experimental Validation
Extensive experiments were conducted on nine diverse real-world datasets, including Electricity, ETT datasets, Exchange, Solar-Energy, and PEMS datasets. FLDmamba consistently demonstrated superior performance, achieving state-of-the-art results in the majority of scenarios compared to a wide range of baselines, including Transformer-based, MLP-based, and other SSM-based methods.
The research also highlighted FLDmamba’s robustness to noise, showing a smaller performance decay when synthetic noise was introduced compared to other methods. Furthermore, FLDmamba proved highly effective in long-term prediction, maintaining stable performance even with increasing lookback window sizes. Case studies visually confirmed its ability to accurately capture both multi-scale periodicity and transient dynamics, outperforming competing models.
This work offers a robust and effective solution for long-term time series prediction, paving the way for its application in various real-world scenarios. For more technical details, you can refer to the full research paper: FLDmamba: Integrating Fourier and Laplace Transform Decomposition with Mamba for Enhanced Time Series Prediction.
